If you by that mean that a ellipse might be seen as a circle under a Lorentz contraction? Because that's what you make me think of :) Then I agree. A circle will become a ellipse when Lorentz contracted, as I think of it.

It's a bit difficult to understand what you are asking, but when you say "entrained space-time", perhaps you are asking if space-time can be dragged around by a spinning object? The answer to that question is yes and is called "frame dragging". The effect has been observed for the Earth itself. In theory, an object moving along an elliptical path instead of a circular one should drag space-time as well.

My question was .If space and time are dragged around ring when the body performs a rotational movement .If the body moves along an ellipse or oval then the space and time are dragged around ellipse or oval ?

Jaiii there are two things creating a time dilation that I know. motion and invariant mass. When a planet orbits some sun it's in a uniform motion, and that one is tricky. Because I like to consider all uniform motions as being the same, relative gravity. Meaning that there is no gravity in a uniform motion.

On the other hand, and it's here I'm not sure, I have to assume that a Lorentz contraction and a time dilation will be existent even after that spaceship turns of its engines. If I don't assume that, you will only see a time dilation and Lorentz contraction existing in cases of acceleration, which makes it very strange to me.

So, in this case we either have to assume that a planets orbital is a combined result of its invariant mass (gravitational potential), and relative motion. Or that it's only a result of invariant mass, its relative uniform motion having no effect as all uniform motion is being 'at rest' relative gravity. Meaning that they all are weight less, following a geodesic.

The frame dragging is about how planets relative motion distort the space in which they move. As invariant mass is coupled to gravity, and as we can use a positional system to define those orbits in time, at different positions, we know that this space is no clear 'wind still surface', like the one of a lake for example. Instead the 'surface ripples' constantly, and also follow the way, for example, Earth moves relative its solar system. And as the 'surface' exist in three dimensions, simultaneously, those 'ripples' becomes hard to see. But we could look at streams inside a volume of water, or in a wind tunnel I guess to see similar effects. You could see invariant mass as what chaos math calls 'mystical attractors' of gravity, that and acceleration.==

( WARNING -PURE SPECULATION BEGINS :)

The most confusing thing about it is that if I really want to follow my logic the whole way a time dilation and so also Lorentz contraction can only be the result of 'gravity'. With that gravity coming in two shapes. Acceleration and invariant mass. and if I then also expect gravity to be what creates a distance inside 'Space'? I like it I have to admit, but it becomes a very confusing universe and one where motion gets a totally different meaning. There is one thing that may make it palatable, and that would be if we finally found a way of defining what the 'arrow of time' should be seen as? For us on Earth time is a 'linear' temporal movement in SpaceTime. But it changes relative 'motion' and 'gravity' so we know there has to be something more to it, but what? ( PURE SPECULATION ENDS :)

If throwing off a rotating disk space and time in a circular motion.Body running on an oval or ellipse also entrained space and time on their route?

By.

If the spacetime was flat to begin with the no change in coordinate system can possibly result in a curved spacetime. What you end up with is a set of curvilinear coordinates. E.g. spatial coordinates can be Cartesian in finite region near the center of rotation yet the motion of particles will follow a curved spatial path.

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